BLIND WATERMARKING OF NON-UNIFORM B-SPLINE SURFACES

2008 ◽  
Vol 08 (03) ◽  
pp. 439-454 ◽  
Author(s):  
SHUSEN SUN ◽  
ZHIGENG PAN ◽  
TAE-WAN KIM
Keyword(s):  
Blind Watermarking ◽  
Knot Insertion ◽  
B Spline ◽  
Original Surface ◽  
Spline Surfaces ◽  
Sign Correlation ◽  
Dct Coefficients ◽  
Sample Points ◽  
Watermarking Scheme ◽  
Correlation Detector

In this paper, we propose a watermarking scheme for non-uniform B-spline (NUBS) surface. Firstly, we first do sampling on a NUBS surface and get the sample points, then the watermark is embedded into the DCT coefficients of the sample points and the watermarked sample points are transformed back, finally the watermarked surface is reconstructed from watermarked sample points using global interpolation. A sign correlation detector is used to test for the presence of the watermark, and the original surface is not required at this stage. Experimental results show that our algorithm can preserve the shape of the original surface within a specified error, and that it is robust against attacks including knot insertion, order elevation, addition of white noise, rotation, scaling, translation and further watermarking.

B2: An Interactive Quality Visualization and Improvement Technique for B-Spline Surfaces

1998 ◽  
Author(s):  
Yifan Chen ◽  
Klaus-Peter Beier
Keyword(s):  
Surface Quality ◽  
Control Points ◽  
Small Surface ◽  
B Spline ◽  
Original Surface ◽  
Interactive Technique ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Surface Irregularities

Abstract A new interactive technique for B-spline surface quality visualization and improvement, called the B2 method, is presented. This method interpolates the control points of a given B-spline surface using a second B-spline surface. If small irregularities exist in the control points of the original surface, they will be magnified through the second B-spline and demonstrated as large distortions in its control points. This facilitates the detection of small surface irregularities. Subsequently, the surface may be improved through direct and interactive adjustment of the second B-spline’s control polyhedron.

Optimization of Geometrically Trimmed B-Spline Surfaces

2005 ◽  
Author(s):  
Xinyu Zhang ◽  
Yaohang Li ◽  
Arvid Myklebust ◽  
Paul Gelhausen
Keyword(s):  
Optimization Method ◽  
Objective Functions ◽  
Global Optimization Method ◽  
Initial Value ◽  
B Spline ◽  
Original Surface ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Approximation Errors ◽  
High Degree

Unlike the visual trimming of B-spline surfaces, which hides unwanted portions in rendering, the geometric trimming approach provides a mathematically clean representation without redundancy. However, the process may lead to significant deviation from the corresponding portion on the original surface. Optimization is required to minimize approximation errors and obtain higher accuracy. In this paper, we describe the application of a novel global optimization method, so-called hybrid Parallel Tempering (PT) and Simulated Annealing (SA) method, for the minimization of B-spline surface representation errors. The high degree of freedom within the configuration of B-spline surfaces as well as the “rugged” landscapes of objective functions complicate the error minimization process. The hybrid PT/SA method, which is an effective algorithm to overcome the slow convergence, waiting dilemma, and initial value sensitivity, is a good candidate for optimizing geometrically trimmed B-spline surfaces. Examples of application to geometrically trimmed wing components are presented and discussed. Our preliminary results confirm our expectation.

Geometric Design and Fabrication of Developable Bezier and B-spline Surfaces

1994 ◽  
Vol 116 (4) ◽  
pp. 1042-1048 ◽  
Author(s):  
R. M. C. Bodduluri ◽  
B. Ravani
Keyword(s):  
Spline Interpolation ◽  
Geometric Design ◽  
Developable Surface ◽  
Knot Insertion ◽  
B Spline ◽  
Developable Surfaces ◽  
Spline Surfaces ◽  
Insertion Algorithm ◽  
Cad Cam ◽  
Type Construction

In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop a direct representation of developable surfaces in terms of plane geometry. It uses control planes to determine a surface which is a Bezier or a B-spline interpolation of the control planes. In the Bezier case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot insertion algorithm are presented. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

2021 ◽  
pp. 1-28
Author(s):  
Dennis Mosbach ◽  
Katja Schladitz ◽  
Bernd Hamann ◽  
Hans Hagen
Keyword(s):  
Degrees Of Freedom ◽  
Tangent Plane ◽  
Local Approach ◽  
Approximation Process ◽  
Surface Approximation ◽  
B Spline ◽  
Spline Surfaces ◽  
Continuous Surface ◽  
Normal Vectors ◽  
The Individual

Abstract We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.

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